The known 4 PN Hamiltonians [1]}, [2]}, [3]}, [4]}, [5]} in harmonic
and ADM coordinates are connected by canonical transformations to \(H_{\rm EOB}\) , cf. [5]},which
imply the expansion parameters
\({\rm N}, u~: &~a_1 &=&~-2,\\{\rm 2PN}, u^2: &~d_2 &=&~6 \nu ,\\u^3: &~a_3 &=&~2 \nu ,\\{\rm 3PN}, u^2: &~q_{42} &=&~ 8 \nu - 6 \nu ^2,\\u^3: &~d_3 &=&~ 52 \nu - 6 \nu ^2,\\u^4: &~a_4 &=&~\left(\frac{94}{3} - \frac{41}{32} \pi ^2\right) \nu ,\\{\rm 4PN}, u^2: &~q_{62} &=&~-\frac{9}{5} \nu - \frac{27}{5} \nu ^2 + 6 \nu ^3,\\u^3: &~q_{43} &=&~20 \nu -83 \nu ^2 +10 \nu ^3,\\u^4: &~d_4 &=&~ \left(\frac{1679}{9} - \frac{23761}{1536} \pi ^2\right) \nu + \left(- 260 + 123 \pi ^2\right) \nu ^2.\) 
